The discussion of topo-centric position of the Moon (lunar parallax) came up over 10 years ago when some persons wanted to use it for calculating mahadasha (planetary periods) in Vedic astrology thinking it would be more accurate. Their rational was that people of the past were ignorant and did not understand the principle of topo-centric versus geocentric. I was going to write an in depth article to counter that view but then the enthusiasm for the topo-centric method sort of died out so I didn’t invest the time and energy to make a presentation. It seems to have reared its head again so at a time of my choosing I will make a full and elaborate presentation on the subject. But for now I will just make a few brief comments.
Vedic Siddhantik astronomy is a geocentric system and all measurements are taken with respect to the center of the earth’s sphere, to the center of the other planets. Using this method the Surya Siddhanta in chapter 1-2 first teach how to find the mean and then the true positions of the planets.
In chapter 2 of Bhakti Siddhanta’s translation of Surya Siddhanta and in chapter 3 of the Gangooly (Burgess) edition it explains how to calculate lunar tithis using the previously calculated true position of the Sun and Moon.
After the discussion of how to find the true position of the planets comes the discussion of special phenomena, eclipses, that requires us to take into consideration the fact that the Sun, Moon and Earth are large spheres . Then and only then do we have to take into account parallax .
“Parallax has been considered in the text [Surya Siddhanta] in a special context, and not as a general astronomical entity. The text has devoted ch.v to discuss the relative parallax of the moon with respect to the sun when an eclipse is due, i.e. the moon is in a conjunction with the sun at a node, or, as the text says, the moon has no latitude.” (Chakravarty, p. 105) Emphasis mine.
Thus the Surya Siddhanta and other siddhantik texts only use parallax (lambana in Sanskrit) in a special context (eclipses) but not for general use such as calculating position of planets.
Eclipses and parallax are discussed in chapters 4-6 of the Surya Siddhanta after the method of finding the true position of the planets is explained. It tells us that to determine if there will be an eclipse one must first find out when the true positions (of the centers) of the Sun, Moon and Earth will be collinear. This can only take place when the Sun and Moon are conjunct the Nodes (Rahu/Ketu). Then parallax of the Sun and Moon are calculated and added to the true places of the Sun and Moon and used to calculate when the shadow will fall on the Sun or Moon depending on which type of eclipse it is.
In conclusion according to Surya Siddhanta and other standard astronomical texts the true positions of the planets are used for determining their longitude, latitude and declination, which in turn is used for calculating lunar tithis. And, that parallax (topocentric position of the Moon) is restricted for use in a special context only, calculating an eclipse, and not for other uses.
This is the default position of the Vedic tradition of astronomy and the method used by our purva acaryas especially HDG Bhakti Siddhanta Sarasvati Thakura a great astronomical genius. I prefer to follow in the footsteps of our previous acaryas.
At a later date, if time permits, I will make a more elaborate presentation. In the mean time I hope what I have provided thus far satisfies the gentle reader.
dasa dasa anu dasa
1 This is not required for the other planets that, because of their distance, appear very small.
2 Topo-centric is equivalent to Lunar Parallax http://en.wikipedia.org/wiki/Parallax#Lunar_parallax
Chakravarty, A.K., 2001, The Suryasiddhanta, Kolkata, The Asiatic Society.